The invention relates to a method to compensate for spectral shift associated with spectrophotometric measurements, more particularly to an iterative method using least squares procedure with differentiation for a multicomponent analysis that reduces noise propagation.
It is often desired to isolate and determine the presence and/or concentration of a particular element or species contained in a sample. For example, in the field of biotechnology, nucleic acid sequence analysis is becoming increasingly important in many research, medical, and industrial fields, e.g. Caskey, Science 236: 1223-1228 (1987); Landegren et al, Science, 242: 229-237 (1988); and Arnheim et al, Ann. Rev. Biochem., 61: 131-156 (1992). The development of several nucleic acid amplification schemes has played a critical role in this trend, e.g. polymerase chain reaction (PCR), Innis et al, editors, PCR Protocols (Academic Press, New York, 1990); McPherson et al, editors, PCR: A Practical Approach (IRL Press, Oxford, 1991); ligation-based amplification techniques, Barany, PCR Methods and Applications 1: 5-16 (1991); and the like.
PCR in particular has become a research tool of major importance with applications in cloning, analysis of genetic expression, DNA sequencing, genetic mapping, and drug discovery, e.g. Arnheim et al (cited above); Gilliland et al, Proc. Natl. Acad. Sci., 87: 2725-2729 (1990); Bevan et al, PCR Methods and Applications, 1: 222-228 (1992); Green et al, PCR Methods and Applications, 1: 77-90 (1991); Blackwell et al, Science, 250: 1104-1110 (1990).
Fluorescence-based approaches to provide real time measurements of amplification products during a PCR have been used. See Holland et al, Proc. Natl. Acad. Sci., 88: 7276-7280 (1991). Such approaches have either employed intercalating dyes (such as ethidium bromide) to indicate the amount of double stranded DNA present, or they have employed probes containing fluorescent-quencher pairs (the so-called xe2x80x9cTaq-Manxe2x80x9d approach) that are cleaved during amplification to release a fluorescent product whose concentration is proportional to the amount of double stranded DNA present.
Spectrometric analysis for quantification of a component in a multicomponent system can be accomplished by measurement at multiple wavelengths such as in inductively coupled plasma optical emission spectroscopy (OES). One of the major problems in handling spectral data of this type arises from overlapped responses from various chemical species in a mixture. See U.S. Pat. No. 5,308,982 to Ivaldi et al., incorporated herein by reference. In the case of PCR analysis, as more targets are sought to be identified in a multicomponent analysis, more fluorescent dyes are used simultaneously. The spectral peaks of different fluorescent dyes tend to overlap to varying degrees to begin with, and as more dyes are used simultaneously, their respective peaks necessarily become closer together in terms of wavelength. As such peaks become closer together, the likelihood of component xe2x80x9ccross-talkxe2x80x9d (i.e, the correlation among estimated concentrations of various components) resulting from an improper component fit increases correspondingly.
Another problem arises from a phenomenon known as xe2x80x9cspectral shiftxe2x80x9d where the measured wavelength of the component shifts. Such shifts cause the peaks of components in the sample to appear to be at different wavelengths than the previously recorded peaks of the pure components. Such apparent shifts may occur, for example, between instruments and even, with time, in the same instrument. In the case of PCR analysis, such spectral shift can be caused by a number factors related to the chemistry of the reaction (i.e. pH change), as well as the instrument hardware. When spectral shift occurs in a PCR analysis, the xe2x80x9cpure dyexe2x80x9d or pure component signals are shifted slightly in terms of wavelength (i.e., they peak at a slightly different frequency) as compared to their appearance when measured individually or at the start of the reaction. Such a phenomenon has a detrimental effect on the accuracy of DNA sequence analysis and quantification since spectral shift can alter the degree of overlap among dye peaks, thereby increasing the likelihood of component cross-talk.
In dealing with the problem of spectral shift generally, the prior art approach has been to use interpolation. The spectral information is collected at discrete points. If a wavelength shift is required, it is necessary to know what the data is between such points. However, since the amount of interpolation is not known, it is required to successively check the error and iterate. This also is a mathematically and time intensive procedure.
U.S. Pat. No. 5,023,804 (Hoult) discloses comparing spectral data with a standard spectrum by computing a normalized dot product of a sample spectrum and the standard spectrum. The two spectra are weighted by filtering to remove short and long periodicities, the filtering being effected with a triangular wave using a simplified algorithm.
U.S. Pat. No. 4,997,280 (Norris) discloses a spectrophotometric instrument in which rapid scanning causes distortion of the spectrum. A first derivative is determined from the spectrum and multiplied by a constant selected to correct for the distortion. The resulting product values are added to the distorted spectrum to provide a set of corrected values for intensity. The selected constant is determined by comparing data acquired from operation of the instrument at a normally rapid speed and then slowly, in order to eliminate the distortion.
Another prior art method uses the Kalman filter, as disclosed in an article xe2x80x9cSome Spectral Interference Studies Using Kalman Filtering in Inductively Coupled Plasma-Atomic Emission Spectroscopyxe2x80x9d by E. H. van Veen, F. J. Oukes and M. T. C. de Loos-Vollebregt, Spectrochimica Acta 45B, 1109-1120 (1990). This is an iterative process. A set of coefficients is estimated. These coefficients are employed to multiply each data point in the spectrum. The error between the results and each data point is computed. A derivative is then estimated that indicates the direction in which to shift the estimates of the coefficients. Accordingly, there is a successive refinement of the error which, after many iterations, converges.
U.S. Pat. No. 5,308,982 (Ivaldi et al.) discloses a method which incorporates a derivative of sample spectral data into a matrix model to compensate for spectral shift. This is a standardization that requires spectral data to be acquired in relatively small spectral increments to achieve sufficient representation of the derivative in the model. Wavelength increments of spectral data ordinarily are limited by pixel size of the detector. Smaller increments are achieved by slit scanning in which the inlet slit to the spectrometer is imaged on a pixel. Varying the lateral position of the slit in small steps effectively moves a spectrum across the pixels to obtain spectral data in smaller increments. Although utilized for collecting archive data, it is preferable that slit scanning be avoided to speed up ordinary data acquisition.
One of the problems with the aforementioned methods is that they are computational and time intensive, requiring many iterations. This becomes a particular problem in the case of real time quantification with spectra collected at 96 Hz or more.
Another problem with the prior methods for spectral compensation, such as those including differentiation, is the propagation of noise. For example, a first derivative for each pure component signal in a multicomponent matrix can be calculated to improve the fit for the spectral shift. While this approach has worked reasonably well, it unfortunately adds a considerable amount of noise to the calculated pure components due to the increased spectral overlaps among the increased number of components and their derivatives.
What is desired, therefore, is a method and apparatus to detect the concentrations of species in a multicomponent mixture which is less computational and time intensive, corrects for spectral shift and reduces the propagation of noise in the computation.
Accordingly, an object of the invention is to provide a method for the analysis of spectral signals for a multicomponent mixture in order to calculate the quantities of the individual components.
Another object of the invention is to provide a method which resolves overlapping spectral responses of a mixture containing a plurality of spectrally independent species.
A further object of the invention to provide a method applying a linear regression technique in which pure component signals are fit to raw measured spectral data of a multicomponent system using a least squares approach.
Yet another object of the invention is to provide a method which corrects for spectral shift in a spectral analysis that is less computational and time intensive.
Another object of the invention is to provide a spectrometric method to calculate the quantities of individual components in a multicomponent mixture which reduces the propagation of noise.
To overcome some of the disadvantages of the prior art and achieve at least some of the objects and advantages listed above, the present invention comprises: a method for compensating for spectral shift in the spectrometric analysis of a sample; and in another aspect, a method for resolving a signal into at least one separate component and compensating for a signal shift in the analysis of a sample, and in a further aspect, an apparatus for compensating for spectral shift in the spectrometric analysis of a sample.
A method according to the invention for compensating for spectral shift in the spectrometric analysis of a sample comprises steps of: obtaining a first set of data corresponding to a spectrum of the sample; retrieving a second set of data corresponding to spectra for at least one pure component of the spectrum; calculating a first derivative for the second set of data; resolving the first set of data into the second set of data, the first derivative, and at least one concentration co-efficient for the pure component; pre-shifting the second set of data to compensate for the spectral shift; further calculating a residual error associated with the spectral shift for the first set of data; comparing the residual error with a pre-determined value; and repeating the pre-shifting, further calculating and comparing steps until the residual error is within the pre-determined value.
The invention in one of its aspects also provides a method for resolving a signal into at least one separate component and compensating for a signal shift in the analysis of a sample comprising steps of: resolving the signal into a first set of data of at least one separate component and a second set of data of at least one coefficient for the separate component; retrieving the first set of data corresponding to the component of the sample; calculating a first derivative for the first set of data; second resolving the signal into the first set of data, the second set of data, and the first derivative; pre-shifting the first set of data to compensate for the signal shift; further calculating a residual error associated with the signal shift for the signal; and comparing the residual error with a pre-determined value; and repeating the pre-shifting, further calculating and comparing steps until the residual error is within the pre-determined value.
In another aspect, the invention provides an apparatus for compensating for spectral shift in the spectrometric analysis of a sample comprising: a device for obtaining a spectrum of the sample; a computer linked to the device; software executing on the computer for obtaining a first set of data corresponding to the spectrum of the sample; software executing on the computer for retrieving a second set of data corresponding to spectra for at least one pure component of the spectrum; software executing on the computer for calculating a first derivative for the second set of data; software executing on the computer for resolving the first set of data into the second set of data, the first derivative, and at least one concentration coefficient for the pure component; software executing on the computer for pre-shifting the second set of data to compensate for the spectral shift; software executing on the computer for further calculating a residual error associated with the spectral shift for the first set of data; software executing on the computer for comparing the residual error with a pre-determined value; and software executing on the computer for repeating the pre-shifting, further calculating and comparing steps until the residual error is within the pre-determined value.
In another aspect of the invention, the method and apparatus comprise the step of further resolving the first set of data into the second set of data and at least one concentration coefficient for the pure component without use of the first derivative.
The invention and its particular features will become more apparent from the following detailed description with reference to the accompanying drawings.